Two vessel A and B of equal capacity contains mixture of milk and water in the ratio 8:y and 7:6 respectively. If total quality of each vessel is 260L and quantity of milk in A is `14 2/7 `%. More than quantity of milk of milk in B then find y

Options

A. A)10
B. B)4
C. C)5
D. D)6

Answer

To solve the problem step by step, we will analyze the information given and perform the necessary calculations.

### Step 1: Understand the Ratios and Total Quantity
We have two vessels, A and B, each with a total capacity of 260 liters. The mixture in vessel A has a milk to water ratio of 8:y, and in vessel B, the ratio is 7:6.

### Step 2: Calculate the Quantity of Milk and Water in Vessel B
First, we need to find out how much milk and water is in vessel B.

- The total parts in the ratio of vessel B (7 parts milk + 6 parts water) = 13 parts.
- Each part = Total quantity / Total parts = 260 liters / 13 = 20 liters.

Now, we can find the quantities:
- Milk in vessel B = 7 parts = 7 * 20 = 140 liters.
- Water in vessel B = 6 parts = 6 * 20 = 120 liters.

### Step 3: Calculate the Quantity of Milk in Vessel A
According to the problem, the quantity of milk in vessel A is 14 2/7% more than the quantity of milk in vessel B.

- Convert 14 2/7% to a fraction:
\[ 14 \frac{2}{7} \% = \frac{100}{7} \% \]
This means that the quantity of milk in A is:
\[ \text{Milk in A} = \text{Milk in B} + \left(\frac{100}{7} \% \text{ of Milk in B}\right) \]
\[ = 140 + \left(\frac{100}{7} \times \frac{140}{100}\right) = 140 + \frac{140}{7} = 140 + 20 = 160 \text{ liters} \]

### Step 4: Calculate the Quantity of Water in Vessel A
Now, since the total quantity in vessel A is 260 liters, we can find the quantity of water:
\[ \text{Water in A} = \text{Total in A} - \text{Milk in A} = 260 - 160 = 100 \text{ liters} \]

### Step 5: Set Up the Ratio for Vessel A
We know the ratio of milk to water in vessel A is 8:y. We can set up the equation:
\[ \frac{8}{y} = \frac{160}{100} \]

### Step 6: Cross Multiply to Solve for y
Cross multiplying gives us:
\[ 8 \times 100 = 160 \times y \]
\[ 800 = 160y \]
\[ y = \frac{800}{160} = 5 \]

### Conclusion
Thus, the value of y is 5.